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Golomb Rulers Roger C. Alperin
 

Summary: Golomb Rulers
Roger C. Alperin
San Jose State University
San Jose, CA 95192
alperin@math.sjsu.edu
Vladimir Drobot
Department of Computer Science
San Jose State University
San Jose, CA 95192
drobot@pacbell.net
The Math Factor podcast posed the problem of finding the smallest num-
ber of inch marks on a 12 inch ruler so that one could still measure any integer
length from 1 to 12. One needs only four additional marks besides 0 and 12;
for example 1, 4, 7, 10 works. This entertaining problem lead to others dur-
ing the next few minutes (you can listen at mathfactor.uark.edu/2005/10)
and inspired us to look for generalizations. After several false starts and
numerous literature searches we uncovered the fascinating theory of Golomb
and minimal spanning rulers, a generalization to the natural numbers and
relations to an unsolved conjecture of Erd¨os and Turan.
We begin the discussion with our first problem--­ which led us to Golomb

  

Source: Alperin, Roger C. - Department of Mathematics, San Jose State University

 

Collections: Mathematics